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right angle wanted, starting with 2 intersecting circles

Source: Indonesia INAMO Shortlist 2009 G5 https://artofproblemsolving.com/community/c1101409_

December 11, 2021
geometrycirclesright angle

Problem Statement

Two circles intersect at points AA and BB. The line ℓ\ell through A intersects the circles at CC and DD, respectively. Let M,NM, N be the midpoints of arc BCBC and arc BDBD. which does not contain AA, and suppose that KK is the midpoint of the segment CDCD . Prove that ∠MKN=90o\angle MKN=90^o.
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